You can make a quadratic function by dragging the three RED points [i]almost[/i] anywhere on the screen (why [i]almost[/i]?). The function will have the form [br][br]quadratic(x) = [math]Ux^2 + Vx + C[/math],[br][br]where U and V are real numbers and the value of C is a real number.[br][br]Now try to build the same quadratic function by combining the appropriate amounts of quadratic term, linear term and constant term using the BLUE sliders. [br]Try to do this without displaying the functional form of the RED quadratic function you have made.[br][br]You can check your work by showing the expressions for the functions on the screen.[br][br]CHALLENGE - A student asks "How do you know that you can always make a quadratic function given three points?" What do you respond?[br][br]Can three points define any other kind of function? How many RED dots would you need to make a cubic function? How do you know?[br][br]A student asks “Is there a way to think about slope for a quadratic function?” What do you respond?[br][br][i][b][color=#ff0000]What questions could/would you pose to your students based on this applet ?[/color][/b][/i]